Method of Artificial Nueral Network Loadflow computation for electrical power system

ABSTRACT

Neural Network Loadflow (NNL) computation method is invented involving input vector composed of net nodal injection of real and reactive powers and diagonal elements of conductance and susceptance matrices multiplied by the squared voltage magnitude components of the flat-start normally used as initial solution estimate guess for loadflow solution by conventional NRL or SSDL methods. Training, and testing/validating input-output data sets are generated by applying uniform and non-uniform scaling factors applied to base case loads at PQ-nodes, resistance and reactance of transmission line branches. These scale factors are increased until loadflow solution by conventional methods such as Newton-Raphson Loadflow and Super Super Decoupled Loadflow methods diverge. Divergence of loadflow methods are due to node voltage, node angle, and numerical instabilities. Voltage magnitude and phase angle values in the solution before divergence are respective stability limits and voltage magnitude and phase angle values in loadflow solution provide direct measure to the respective stability margins. Also Suresh&#39;s diakoptiks based feature selection technique is presented for ANNs calculating one node variable with one neuron each in their output layers.

TECHNICAL FIELD

The present invention relates to method of Artificial Neural Network Loadflow (ANNL) computation in power flow control and voltage control in an electrical power system.

BACKGROUND OF THE INVENTION

The present invention relates to power-flow/voltage control in utility/industrial power networks of the types including many power plants/generators interconnected through transmission/distribution lines to other loads and motors. Each of these components of the power network is protected against unhealthy or alternatively faulty, over/under voltage, and/or over loaded damaging operating conditions. Such a protection is automatic and operates without the consent of power network operator, and takes an unhealthy component out of service by disconnecting it from the network. The time domain of operation of the protection is of the order of milliseconds.

The purpose of a utility/industrial power network is to meet the electricity demands of its various consumers 24-hours a day, 7-days a week while maintaining the quality of electricity supply. The quality of electricity supply means the consumer demands be met at specified voltage and frequency levels without over loaded, under/over voltage operation of any of the power network components. The operation of a power network is different at different times due to changing consumer demands and development of any faulty/contingency situation. In other words healthy operating power network is constantly subjected to small and large disturbances. These disturbances could be consumer/operator initiated, or initiated by overload and under/over voltage alleviating functions collectively referred to as security control functions and various optimization functions such as economic operation and minimization of losses, or caused by a fault/contingency incident.

For example, a power network is operating healthy and meeting quality electricity needs of its consumers. A fault occurs on a line or a transformer or a generator which faulty component gets isolated from the rest of the healthy network by virtue of the automatic operation of its protection. Such a disturbance would cause a change in the pattern of power flows in the network, which can cause over loading of one or more of the other components and/or over/under voltage at one or more nodes in the rest of the network. This in turn can isolate one or more other components out of service by virtue of the operation of associated protection, which disturbance can trigger chain reaction disintegrating the power network.

Therefore, the most basic and integral part of all other functions including optimizations in power network operation and control is security control. Security control means controlling power flows so that no component of the network is over loaded and controlling voltages such that there is no over voltage or under voltage at any of the nodes in the network following a disturbance small or large. As is well known, controlling electric power flows include both controlling real power flows which is given in MWs, and controlling reactive power flows which is given in MVARs. Security control functions or alternatively overloads alleviation and over/under voltage alleviation functions can be realized through one or combination of more controls in the network. These involve control of power flow over tie line connecting other utility network, turbine steam/water/gas input control to control real power generated by each generator, load shedding function curtails load demands of consumers, excitation controls reactive power generated by individual generator which essentially controls generator terminal voltage, transformer taps control connected node voltage, switching in/out in capacitor/reactor banks controls reactive power at the connected node.

Control of an electrical power system involving power-flow control and voltage control commonly is performed according to a process shown in FIG. 7, which is a method of forming/defining a loadflow computation model of a power network to affect control of voltages and power flows in a power system comprising the steps of:

Step-10: obtaining on-line/simulated data of open/close status of all switches and circuit breakers in the power network, and reading data of operating limits of components of the power network including maximum power carrying capability limits of transmission lines, transformers, and PV-node, a generator-node where Real-Power-P and Voltage-Magnitude-V are given/assigned/specified/set, maximum and minimum reactive power generation capability limits of generators, and transformers tap position limits, or stated alternatively in a single statement as reading operating limits of components of the power network,

Step-20: obtaining on-line readings of given/assigned/specified/set Real-Power-P and. Reactive-Power-Q at PQ-nodes, Real-Power-P and voltage-magnitude-V at PV-nodes, voltage magnitude and angle at *a reference/slack node, and transformer turns ratios, wherein said on-line readings are the controlled variables/parameters,

Step-30: performing loadflow computation to calculate, depending on loadflow computation model used, complex voltages or their real and imaginary components or voltage magnitudes or their corrections and voltage angles or their corrections at nodes of the power network providing for calculation of power flow through different components of the power network, and to calculate reactive power generation and transformer tap-position indications,

Step-40: evaluating the results of Loadflow computation of step-30 for any over loaded power network components like transmission lines and transformers, and over/under voltages at different nodes in the power system,

Step-50: if the system state is acceptable implying no over loaded transmission lines and transformers and no over/under voltages, the process branches to step-70, and if otherwise, then to step-60,

Step-60: correcting one or more controlled variables/parameters set in step-20 or at later set by the previous process cycle step-60 and returns to step-30,

Step-70: affecting a change in power flow through components of the power network and voltage magnitudes and angles at the nodes of the power network by actually implementing the finally obtained values of controlled variables/parameters after evaluating step finds a good power system or stated alternatively as the power network without any overloaded components and under/over voltages, which finally obtained controlled variables/parameters however are stored for acting upon fast in case a simulated event actually occurs or stated alternatively as actually implementing the corrected controlled variables/parameters to obtain secure/correct/acceptable operation of power system.

Overload and under/over voltage alleviation functions produce changes in controlled variables/parameters in step-60 of FIG. 7. In other words controlled variables/parameters are assigned or changed to the new values in step-60. This correction in controlled variables/parameters could be even optimized in case of simulation of all possible imaginable disturbances including outage of a line and loss of generation for corrective action stored and made readily available for acting upon in case the simulated disturbance actually occurs in the power network. In fact simulation of all possible imaginable disturbances is the modern practice because corrective actions need be taken before the operation of individual protection of the power network components.

It is obvious that loadflow computation consequently is performed many times in real-time operation and control environment and, therefore, efficient and high-speed loadflow computation is necessary to provide corrective control in the changing power system conditions including an outage or failure of any of the power network components. Moreover, the loadflow computation must be highly reliable to yield converged solution under a wide range of system operating conditions and network parameters. Failure to yield converged loadflow solution creates blind spot as to what exactly could be happening in the network leading to potentially damaging operational and control decisions/actions in capital-intensive power utilities.

The power system control process shown in FIG. 7 is very general and elaborate. It includes control of power-flows through network components and voltage control at network nodes. However, the control of voltage magnitude at connected nodes within reactive power generation capabilities of electrical machines including generators, synchronous motors, and capacitor/inductor banks, and within operating ranges of transformer taps is normally integral part of loadflow computation as described in “LTC Transformers and MVAR violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No.9, PP. 3328-3332, September 1982.” If under/over voltage still exists in the results of loadflow computation, other control actions, manual or automatic, may be taken in step-60 in the above and in FIG. 7. For example, under voltage can be alleviated by shedding some of the load connected.

The prior art and present invention are described using the following symbols and terms:

Y_(pq)=G_(pq)+jB_(pq): (p-q) th element of nodal admittance matrix without shunts Y_(pp)=G_(pp)+jB_(pp): p-th diagonal element of nodal admittance matrix without shunts y_(p)=g_(p)+jb_(p): total shunt admittance at any node-p V_(p)=e_(p)+jf_(p)=V_(p)∠θ_(p): complex voltage of any node-p P_(p)+jQ_(p): net nodal injected power calculated RP_(p)+jRQ_(p): modified nodal power residue or mismatch Φ_(p): rotation or transformation angle [RP]: vector of modified real power injections at power-network nodes [RQ]: vector of modified reactive power injections at power-network nodes m: number of PQ-nodes k: number of PV-nodes n=m+k+1 : total number of nodes q>p: q is the node adjacent to node-p excluding the case of q=p []: indicates enclosed variable symbol to be a vector or a matrix PQ-node: load-node, where, Real-Power-P and Reactive-Power-Q are specified PV-node: generator-node, where, Real-Power-P and Voltage-Magnitude-V are specified

Loadflow Computation: Each node in a power network is associated with four electrical quantities, which are voltage magnitude, voltage angle, real power, and reactive power. The loadflow computation involves calculation/determination of two unknown electrical quantities for other two given/specified/scheduled/set/known electrical quantities for each node. In other words the loadflow computation involves determination of unknown quantities in dependence on the given/specified/scheduled/set/known electrical quantities.

Loadflow Model: a set of equations describing the physical power network and its operation for the purpose of loadflow computation. The term ‘loadflow model’ can be alternatively referred to as ‘model of the power network for loadflow computation’. The process of writing Mathematical equations that describe physical power network and its operation is called Mathematical Modeling. If the equations do not describe/represent the power network and its operation accurately the model is inaccurate, and the iterative loadflow computation method could be slow and unreliable in yielding converged loadflow computation. There could be variety of Loadflow Models depending on organization of set of equations describing the physical power network and its operation, including Newton Raphson Loadflow (NRL) Model, and Supert Super Decoupled Loadflow (SSDL) Model.

Loadflow Method: sequence of steps used to solve a set of equations describing the physical power network and its operation for the purpose of loadflow computation is called Loadflow Method, which term can alternatively be referred to as ‘loadflow computation method’ or ‘method of loadflow computation’. One word for a set of equations describing the physical power network and its operation is: Model. In other words, sequence of steps used to solve a Loadflow Model is a Loadflow Method. The loadflow method involves definition/formation of a loadflow model and its solution. There could be variety of Loadflow Methods depending on a loadflow model and iterative scheme used to solve the model including Newton Raphson Loadflow (NRL) Methods, Supert Super Decoupled Loadflow (SSDL) Method.

Artificial Neural Network

Neural Network (NN) based prior art loadflow methods of the kind carried out as step-30 in FIG. 4 are described in “Stochastic Load Flow Analysis Using Artificial Neural Networks, 2006 IEEE” by A. Jain, S. C. Tripathy, R. Balasubramanian, and Y. Kawazoe; “Radial basis function neural network for power system load-flow, Electrical Power and Energy Systems 30 (2008) 60-66” by A. Karami and M. S. Mohammadi, and “Artificial neural networks for load flow and external equivalents studies, Electric Power Systems Research (2010) article in press” by H. H. Muller, M. J. Rider and C. A. Castro. In the above publications and others, various type of Artificial Neural Networks (ANNs) involved in loadflow calculation are Multilayer Percepton (MLP), Radial Basis Function (RBF), Counter Propagation (CP) and Hopefied model. Detailed description of various ANNs and their training, and testing or validation process is available in “Principles of Neurocomputing for Science and Engineering, McGrow-Hill (2001)” by Fredric M. Ham and Ivica Kostanic, and Principles of Artificial Neural Networks, World Scientific Publication (2007)” by Daniel Graupe. Testing or validation of a trained ANN is to check if the trained ANN has learned to give accurate enough output vector for a given input vector, which was not used in the training process. It is intended to keep basic description of Artificial Neural Network and its training process short except inventive parts.

ANN is considered as an important technique of artificial intelligence. In recent years, ANNs have gained wide spread attention and they are being used successfully in many areas of power systems. Since the first research paper “Artificial neural-net based dynamic security assessment for electric power systems, IEEE Trans. Power System 4 (1) (1989) 220-226” by D. J. Sobajic and Y. H. Pao published, increasing literature demonstrates the potential of ANN especially in applications that take advantage of the speed of ANNs for on-line calculations and their inherent capacity to overcome modeling complexity. ANN can model any nonlinear function without knowledge of the actual model structure. ANNs can learn complex non-linear relationships through a set of input/output examples, and can approximate nonlinear functional relationship among power system parameters of interest. It can be said that outputs of a conventional loadflow method like NRL or SSDL are functions of the operating conditions of a power system, and ANNs can be employed to approximate these functions. An attractive feature of the ANN loadflow computation is that there is no possibility of non-convergence as it might occur with iterative methods like NRL and SSDL described in “Super Super Decoupled Loadflow, Presented at IEEE International Conference—Science and Technology for Humanity (TIC-STH 2009), pp.252-259” by Suresh B. Patel. Once an ANN is trained, it gives output in negligible time by simple direct arithmetic operations on a given set of inputs of power system operating condition. The ANN Loadflow can replace the conventional NRL and SSDL methods in real time power system operation where time constraints are very restrictive.

Artificial Neural Networks (ANNs) can be considered as information processing systems composed of varying number of simple elements called Neurons distributed into layers. Neurons are organized in an input layer, one or more hidden layers, and an output layer. The connections between elements largely determine network function just as in natural biological nervous systems from which ANNs are inspired. ANN is an intelligent technique that mimics the functioning of a human brain, and emulates human intuition of making decisions and drawing conclusions even when presented with complex, noisy, irrelevant and partial information. The structure of an ANN with only one hidden layer is depicted in FIG. 1, which is generic and abstract with learning, memorizing and adapting characteristic. The neurons in FIG. 1 are connected to each other by weighted links over which signals can pass. Each neuron receives multiple inputs from other neurons, except the neurons in the input layer, in proportion to their connection weights and then generates a single output in accordance with an activation function. An activation function can be linear or nonlinear depending on application. Sigmoid or Hyperbolic Tangent activation function is generally used to improve the performance of ANNs in power system applications.

An ANN can be trained to perform a particular function by adjusting values of the interconnections called weights, and neuron thresholds. The process of adjusting interconnection weights and neuron thresholds to achieve output of the ANN the same as the target value or desired output for a given input as depicted in FIG. 2 is called training of ANN. Training an ANN consists of adjusting interconnection weights of neurons using a learning algorithm. Back propagation with momentum is the commonly used learning algorithm. Multilayer Feed Forward ANNs with Error Back Propagation learning algorithm are commonly used in power system applications. Feed Forward calculations, and propagating error from output layer to input layer and weight updating in hidden and output layers are major steps of training algorithm. ANNs are also referred to as Neural Networks (NNs).

The prior art ANN training process can be divided into four modules. The training and testing process is carried out off-line, and it is the supervised process.

1. Definition of Input and Output vectors: The prior art ANN Loadflow method of

“Artificial neural networks for load flow and external equivalents studies, Electric Power Systems Research (2010) article in press” by H. H. Muller, M. J. Rider and C. A. Castro, suggest the input data vector of dimention 2(m+k+1) given below.

G_(d)=V_(g) ²G_(d) ^(NORM)−P_(L) ^(NORM)+Pg_(pv) ^(NORM)+CV_(p)  (1)

B_(d)=−V_(g) ²B_(d) ^(NORM)−Q_(L) ^(NORM)+CV_(q)  (2)

Where, G_(d) ^(NORM) and B_(d) ^(NORM) are the diagonal elements of conductance and susceptance matrices, normalized with respect to the respective largest element in base case. Load powers P_(L) ^(NORM) and Q_(L) ^(NORM), as well as generation power Pg are also normalized with respect to their base case values. Voltages of generator buses V_(g) are also included.

Contingency information is also added to equations (1) and (2) through CV_(p) and CV_(q). The authors write, “This additional information was included to compensate the loss of information associated to changes in off-diagonal terms of the admittance matrix.” The definition of equations (1) and (2) is given in the same language of authors, which appears to be very confusing.

2. Training and Testing data modeling: The idea of simulating daily load curve is used for generating training and testing datasets. Therefore, for each training and testing demand profile, there is a base case and a set of contingencies, in order to simulate possible cases that could occur in practice. For the training data, the load range is defined as [0.75-1.25] pu. As for testing or simulating data, this range is defined as [0.73-1.27] pu, taking into account that the simulation data should be different from those of training. These load ranges are applied simultaneously for all buses. For each input data set or input vector representing power system operating condition, loadflow calculation by NRL or SSDL method is performed in off line mode to obtain corresponding output data set or output vector. Contingencies that result in islanding, multiple contingencies, voltage magnitudes below 0.75 pu, and angles outside greater and beyond −80° and +80° are not considered for either the training or testing datasets.

3. Run and error control: Each pair of input data set of power system operating condition and corresponding output data set of loadflow calculation used as target or desired output is applied to ANN normally simulated on computer. The process of this step requires initialization minimum number of neurons in hidden layer, and random synaptic weights of interconnections of neurons. Number of neurons in input layer is decided by number of elements of input data set or input vector, and number of neurons in output layer is decided by number of elements of output data set or output vector. With the initialization number of neurons in hidden layer, random synaptic weights of interconnections and application of input vector, feed-forward action of the ANN generates or calulates its output vector, which is compared against the target vector as in FIG. 2. Error of this comparison is feed back by Back Propagation with momentum using steepest gradient descent technique or second order Levenberg-Marquardt algorithm to update the interconnection weights and threshold of neurons. This process is continued iteratively until error produced is acceptably small for all input/output data sets generated for training of ANN. Trained ANN is then tested or validated if it has learned to produce accurate enough output vectors for a given set of input vectors which are different than those used in training. In testing phase, error in output vector is not feedback to update weights of interconnection of neurons. If the error vector in testing phase is not small enough further training is carried out followed again by testing and validating phase. This process training followed by testing and validating is iterated until testing and validating phase produce errors acceptably small enough, and the best ANN is stored in terms of values of interconnection weights, number of neurons in different layers for actual use in solving problems for which it is trained. However, for a given set of inputs the rate of convergence of training and testing process largely depends upon the number of hidden neurons, learning rate, momentum factor, and the initial values of synaptic weights and neuron thresholds. Clearly, the proper choice of all these parameters is very difficult and involves too many trials as well as uncertainties leading to several thousands of iterations for the convergence of training and testing or validating process.

4. Processing Results: Stored ANN in terms of values of interconnection weights, number of neurons in different layers and its performance is analyzed and recorded errors are shown and plotted for future reference and possible use.

Calculation Steps of Prior Art ANNL Method

The steps of ANN Loadflow computation method are shown in the flowchart of FIG. 3. Referring to the flowchart of FIG. 3, different steps are elaborated in steps marked with similar letters in the following. The words “Read system data” in Step-1 correspond to step-10 and step-20 in FIG. 7, and step-14, step-20, step-32, step-44, step-50 in FIG. 8. All other steps in the following correspond to step-30 in FIG. 7, and step-60, step-62, and step-64 in FIG. 8.

a. Read system data

b. Form nodal admittance matrix

c. Form input data vector using equation (1) and (2) for stored ANN, which is trained, tested and validated using steps-1 to 4 in the above.

d. Map (Calculate) high quality and accuracy unadjusted ANN Loadflow output using stored ANN and input data vector

e. Perform NRL or SSDL with control adjustments using high quality initialization loadflow solution yielded by ANN

f. From calculated and known values of voltage magnitude and voltage angle at different power network nodes, and tap position of tap changing transformers, calculate power flows through power network components, and reactive power generation at PV-nodes.

SUMMARY OF THE INVENTION

It is a primary object of the present invention to improve solution efficiency of the prior art SSDL computation method under wide range of system operating conditions and network parameters by invented ANN Loadflow for use in power flow control and voltage control and other controls in the power system.

The above and other objects are achieved, according to the present invention, with Artificial Neural Network Loadflow (ANNL) computation method for Electrical Power System. In context of voltage control, the inventive method of ANNL computation for Electrical Power system consisting of plurality of electromechanical rotating machines, transformers and electrical loads connected in a network, each machine having a reactive power characteristic and an excitation element which is controllable for adjusting the reactive power generated or absorbed by the machine, and some of the transformers each having a tap changing element, which is controllable for adjusting turns ratio or alternatively terminal voltage of the transformer, said system comprising:

means for defining and solving loadflow model of the power network characterized by inventive ANNL model and SSDL model in combination for providing an indication of the quantity of reactive power to be supplied by each generator including the reference/slack node generator, and for providing an indication of turns ratio of each tap-changing transformer in dependence on the obtained-online or given/specified/set/known controlled network variables/parameters, and physical limits of operation of the network components,

means for machine control connected to the said means for defining and solving loadflow model and to the excitation elements of the rotating machines for controlling the operation of the excitation elements of machines to produce or absorb the amount of reactive power indicated by said means for defining and solving loadflow model in dependence on the set of obtained-online or given/specified/set controlled network variables/parameters, and physical limits of excitation elements,

means for transformer tap position control connected to said means for defining and solving loadflow model and to the tap changing elements of the controllable transformers for controlling the operation of the tap changing elements to adjust the turns ratios of transformers indicated by the said means for defining and solving loadflow model in dependence on the set of obtained-online or given/specified/set controlled network variables/parameters, and operating limits of the tap-changing elements.

The method and system of voltage control according to the preferred embodiment of the present invention provide voltage control for the nodes connected to PV-node generators and tap changing transformers for a network in which real power assignments have already been fixed. The said voltage control is realized by controlling reactive power generation and transformer tap positions.

The inventive system of ANNL computation can be used to solve a model of the Electrical Power System for voltage control. For this purpose real and reactive power assignments or settings at PQ-nodes, real power and voltage magnitude assignments or settings at PV-nodes and transformer turns ratios, open/close status of all circuit breaker, the reactive capability characteristic or curve for each machine, maximum and minimum tap positions limits of tap changing transformers, operating limits of all other network components, and the impedance or admittance of all lines are supplied. ANNL model gives output very fast by performing simple arithmetic operations on inputs corresponding to power system operating condition. The output of ANNL is supplied as high quality initial solution estimate to the conventional SSDL model for completing solution with control adjustments incorporated quickly in two to three iterations. During this solution the quantities, which can vary are the real and reactive power at the reference/slack node, the reactive power set points for each PV-node generator, the transformer transformation ratios, and voltages on all PQ-nodes nodes, all being held within the specified ranges. When the iterative process converges to a solution, indications of reactive power generation at PV-nodes and transformer turns-ratios or tap-settings are provided. Based on the known reactive power capability characteristics of each PV-node generator, the determined reactive power values are used to adjust the excitation current to each generator to establish the reactive power set-points. The transformer taps are set in accordance with the turns ratio indication provided by the SSDL computation.

For voltage control, system of ANNL and SSDL computation can be employed either on-line or off-line. In off-line operation, the user can simulate and experiment with various sets of operating conditions and determine reactive power generation and transformer tap settings requirements. An invented parallel computer System can implement any of the parallel loadflow computation methods. For on-line operation, the loadflow computation system is provided with data identifying the current real and reactive power assignments and transformer transformation ratios, the present status of all switches and circuit breakers in the network and machine characteristic curves in steps-10 and -20 in FIG. 7, and steps 12, 20, 32, 44, and 50 in FIG. 8 described below. Based on this information, a model of the system provide the values for the corresponding node voltages, reactive power set points for each machine and the transformation ratio and tap changer position for each transformer.

Inventions include ANNL method involving ANN trained with inventive input vector of variables that take different input values of invented input/output data sets for off-line training and testing.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an Artificial Neural Network (ANN) configuration

FIG. 2 is a block diagram of Artificial Neural Network (ANN) Training

FIG. 3 is a flow chart of prior art Artificial Neural Network Loadflow computation

FIG. 4 is a flow chart of invented Artificial Neural Network Loadflow computation

FIG. 5 is block diagrams of various possible invented ANN configurations

FIG. 6 is a flow-chart of invented ANN Loadflow based security evaluation functions

FIG. 7 is a prior art flow-chart of the overall controlling method for an electrical power system involving loadflow computation as a step which can be executed using one of the invented loadflow computation method of FIG. 4.

FIG. 8 is a prior art flow-chart of the simple special case of voltage control system in overall controlling system of FIG. 7 for an electrical power system

FIG. 9 is a prior art one-line diagram of an exemplary 6-node power network having a reference/slack/swing node, two PV-nodes, and three PQ-nodes

DESCRIPTION OF A PREFERRED EMBODIMENT

A loadflow computation is involved as a step in power flow control and/or voltage control in accordance with FIG. 7 or FIG. 8. A preferred embodiment of the present invention is described with reference to FIG. 6 as directed to achieving voltage control.

FIG. 9 is a simplified one-line diagram of an exemplary utility power network to which the present invention may be applied. The fundamentals of one-line diagrams are described in section 6.11 of the text ELEMENTS OF POWER SYSTEM ANALYSIS, forth edition, by William D. Stevenson, Jr., McGrow-Hill Company, 1982. In FIG. 9, each thick vertical, line is a network node. The nodes are interconnected in a desired manner by transmission lines and transformers each having its impedance, which appears in the loadflow models. Two transformers in FIG. 6 are equipped with tap changers to control their turns ratios in order to control terminal voltage of node-1 and node-2 where large loads are connected.

Node-6 is a reference node alternatively referred to as the slack or swing-node, representing the biggest power plant in a power network. Nodes-4 and -5 are PV-nodes where generators are connected, and nodes-1, -2, and -3 are PQ-nodes where loads are connected. It should be noted that the nodes-4, -5, and -6 each represents a power plant that contains many generators in parallel operation. The single generator symbol at each of the nodes-4, -5, and -6 is equivalent of all generators in each plant. The power network further includes controllable circuit breakers located at each end of the transmission lines and transformers, and depicted by cross markings in one-line diagram of FIG. 9. The circuit breakers can be operated or in other words opened or closed manually by the power system operator or relevant circuit breakers operate automatically consequent of unhealthy or faulty operating conditions. The operation of one or more circuit breakers modify the configuration of the network. The arrows extending certain nodes represent loads.

A goal of the present invention is to provide a reliable and computationally efficient loadflow computation that appears as a step in power flow control and/or voltage control systems of FIG. 7 and FIG. 8. However, the preferred embodiment of loadflow computation as a step in control of node voltages of PV-node generators and tap-changing transformers is illustrated in the flow diagram of FIG. 8 in which present invention resides in function steps 60 and 62.

Short description of other possible embodiment of the present invention is also provided herein. The present invention relates to control of utility/industrial power networks of the types including plurality of power plants/generators and one or more motors/loads, and connected to other external utility. In the utility/industrial systems of this type, it is the usual practice to adjust the real and reactive power produced by each generator and each of the other sources including synchronous condensers and capacitor/inductor banks, in order to optimize the real and reactive power generation assignments of the system. Healthy or secure operation of the network can be shifted to optimized operation through corrective control produced by optimization functions without violation of security constraints. This is referred to as security constrained optimization of operation. Such an optimization is described in the U.S. Pat. No. 5,081,591 dated Jan. 13, 1992: “Optimizing Reactive Power Distribution in an Industrial Power Network”, where the present invention can be embodied by replacing the step nos. 56 and 66 each by a step of constant gain matrices [Yθ] and [YV], and replacing steps of “Exercise Newton-Raphson Algorithm” by steps of “Exercise parallel GSPL or SSDL Computation” in places of steps 58 and 68. This is just to indicate the possible embodiment of the present invention in optimization functions like in many others including state estimation function. However, invention is being claimed through a simplified embodiment without optimization function as in FIG. 8 in this application. The inventive steps-60 and -62 in FIG. 5 are different than those corresponding steps-56, and -58, which constitute a well known Newton-Raphson loadflow method, and were not inventive even in U.S. Pat. No. 5,081,591.

In FIG. 8, function step 10 provides stored impedance values of each network component in the system. This data is modified in a function step 12, which contains stored information about the open or close status of each circuit breaker. For each breaker that is open, the function step 12 assigns very high impedance to the associated line or transformer. The resulting data is than employed in a function step 14 to establish an admittance matrix for the power network. The data provided by function step 10 can be input by the computer operator from calculations based on measured values of impedance of each line and transformer, or on the basis of impedance measurements after the power network has been assembled.

Each of the transformers T1 and T2 in FIG. 9 is a tap changing transformer having a plurality of tap positions each representing a given transformation ratio. An indication of initially assigned transformation ratio for each transformer is provided by function step 20.

The indications provided by function steps 14, and 20 are supplied to a function step 60 in which constant gain matrices [Yθ] and [YV] of the super decoupled loadflow model is constructed, factorized and stored. The gain matrices [Yθ] and [YV] are conventional tools employed for solving Super Decoupled Loadflow model.

Indications of initial reactive power, or Q on each node, based on initial calculations or measurements, are provided by a function step 30 and these indications are used in function step 32, to assign a Q level to each generator and motor. Initially, the Q assigned to each machine can be the same as the indicated Q value for the node to which that machine is connected.

An indication of measured real power, P, on each node is supplied by function step 40. Indications of assigned/specified/scheduled/set generating plant loads that are constituted by known program are provided by function step 42, which assigns the real power, P, load for each generating plant on the basis of the total P, which must be generated within the power system. The value of P assigned to each power plant represents an economic optimum, and these values represent fixed constraints on the variations, which can be made by the system according to the present invention. The indications provided by function steps 40 and 42 are supplied to function step 44 which adjusts the P distribution on the various plant nodes accordingly. Function step 50 assigns initial approximate or guess solution to begin iterative method of loadflow computation, and reads data file of operating limits on power network components, such as maximum and minimum reactive power generation capability limits of PV-nodes generators.

The indications provided by function steps 32, 44, 50 and 60 are supplied to function step 62 where inventive ANNL in combination with SSDL computation is carried out, the results of which appear in function step 64. The loadflow computation yields voltage magnitudes and voltage angles at PQ-nodes, real and reactive power generation by the reference/slack/swing node generator, voltage angles and reactive power generation indications at PV-nodes, and transformer turns ratio or tap position indications for tap changing transformers. The system stores in step 62 a representation of the reactive capability characteristic of each PV-node generator and these characteristics act as constraints on the reactive power that can be calculated for each PV-node generator for indication in step 64. The indications provided in step 64 actuate machine excitation control and transformer tap position control. All the loadflow computation methods using SSDL models can be used to effect efficient and reliable voltage control in power systems as in the process flow diagram of FIG. 8.

Inventions are an invented ANNL method involving ANN trained with inventive input vector of variables that take different input values of invented input/output data sets for off-line training, and testing and validating, and security evaluation functions based on the ANNL method. Inventions achieve unification of loadflow calculations, and steady state security evaluation functions like contingency analysis, and voltage and angle stability evaluations.

An inventive ANN training and testing process can also be divided into four modules. The training and testing process is carried out off-line, and it is the supervised process. The inventive training and testing process differs only in module-1, and module-2 of the four modules listed for the prior art ANN training and testing process in the above. Modules-3 and -4 are the same for both prior art and inventive ANN training and testing process. Therefore, only inventive modules-11, and -12 corresponding to prior modules-1, and -2 are listed in the following description.

11. Definition of Input and Output vectors: Invented input data vector of dimension 2n for ANN loadflow computation is given below as modified scheduled/specified real, RP_(p) and reactive, RQ_(p) power injections at node-p.

RP_(p)=(P_(pg)−P_(p1))−V_(po) ²(G_(pp)+g_(p))  (3)

RQ_(p)=(Q_(pg)−Q_(p1))+V_(po) ²(B_(pp)+b_(p))  (4)

Where, _(p)=_(1, 2, . . . , n) and components of equations (3) and (4) are normalized with respect to the respective largest elements combined or each individually. P_(pg) and Q_(pg) are scheduled/specified real and reactive power generation, and P_(p1) and Q_(p1) are scheduled/specified real and reactive power load/demand at node-p. Flat-start is the same voltage angle of zero radian at all nodes, and scheduled/specified voltage magnitude at respective generation node and reference/slack node and voltage magnitude of 1.0 pu at all load nodes, which is conventionally used as initial starting solution guess for classical NRL and SSDL loadflow computation methods. V_(po) in equations (3) and (4) is the flat-start voltage magnitude at node-p. Flat-start. Algebraic signs − and + preceding V_(po) ² in equations (3) and (4) can also alternatively take + and − signs respectively. Components of output vector consists of estimated voltage angles at PQ-nodes+PV-nodes, voltage magnitudes at PQ-nodes, reactive power generation at PV-nodes, V-stability index/margin and θ-stability index/margin at PQ-nodes. These invented input/output vectors or data sets are depicted in FIG. 5 for various ANN configurations.

12. Training and Testing data modeling: The idea of simulating feasible and continuous non-linearity operating region of power system is used for generating training and testing datasets. Therefore, for each training and testing demand profile, there is a base case and a set of contingencies, in order to simulate possible cases that could occur in practice. These data sets are generated by simulating different loading, and network parametric including contingent conditions by running conventional NRL or SSDL program off-line. The training and testing data sets generated are listed in the following.

1) From the base case loading condition, multiply real power loading at all nodes simultaneously by a factor above 1.0, increasing in any step size (say 0.5) until loadflow solution diverges reaching the θ-stability limit.

2) From the base case loading condition, multiply reactive power loading at all nodes simultaneously by a factor above 1.0, increasing in any step size (say 0.5) until loadflow solution diverges reaching the V-stability limit.

3) From the base case loading condition, multiply real power loading at all nodes simultaneously by a factor above 1.0, increasing in any step size (say 0.5) until loadflow solution diverges reaching the θ-stability limit. This time distributing total increased real power loading on to generators in proportion to their participating factor in base case loading.

4) The above three loading scenarios are repeated by application of increased real or reactive loading at individual PQ-node one at a time.

5) Any contingency situation will probably land somewhere in feasible and continuous non-linearity operating region of power system operating scenarios generated by four items listed in the above. Therefore, credible contingencies are simulated only in base case operating condition. However, they can always be simulated for carefully selected any other loading'scenarios if required.

6) Variations in power network parametric condition are simulated by uniform and non-uniform application of scale factors to base case impedances of branches. R-scale factors are applied to resistances, and x-scale factors are applied to reactances.

7) Under all possible operating condition, reactive power load at each node one at a time is increased until loadflow solution diverges in order to determine V-stability margin for each node from the actual reactive power load under current operating condition. Similarly, real power load at each node one at a time is increased until loadflow solution diverges in order to determine θ-stability margin for each node from the actual real power load under current operating condition.

8) The extensive datasets generated as in items 1) to 7) in the above are randomized while applying to ANN for training and testing purpose, 80% of which is used for training and the remaining 20% used for testing and validation.

The scale factors are increased until loadflow solution by conventional methods such as NRL or SSDL methods diverge. Divergence of loadflow methods are due to numerical or node voltage or node angle instabilities. Voltage magnitude and phase angle values in the solution before divergence are respective stability limits and voltage magnitude and phase angle values in loadflow solution provide direct measure to the respective stability margins. For each input data set or input vector representing power system operating condition, loadflow calculation by NRL or SSDL method is performed in off line mode to obtain corresponding output data set or output vector. Contingencies that result in islanding, and multiple contingencies, are not considered for either the training or testing datasets.

Calculation Steps of Invented ANNL Method

The steps of an invented ANN Loadflow computation method are shown in the flowchart of FIG. 4. Referring to the flowchart of FIG. 4, different steps are elaborated in steps marked with similar letters in the following. The words “Read system data” in Step-a correspond to step-10 and step-20 in FIG. 7, and step-14, step-20, step-32, step-44, step-50 in FIG. 8. All other steps in the following correspond to step-30 in FIG. 7, and step-60, step-62, and step-64 in FIG. 8. It should be noted that only double lettered step-cc of the invented ANN loadflow method differs from those of prior art method.

a. Read system data

b. Form nodal admittance matrix

cc. Form input data vector using equation (1) and (2) for stored ANN, which is trained, tested and validated using step-11, step-12, step-3, and step-4 in the above.

d. Map (Calculate) high quality and accuracy unadjusted ANN Loadflow output using stored ANN and input data vector

e. Perform NRL or SSDL with control adjustments using high quality initialization loadflow solution yielded by ANN

g. From calculated and known values of voltage magnitude and voltage angle at different power network nodes, and tap position of tap changing transformers, calculate power flows through power network components, and reactive power generation at PV-nodes.

Feature Selection Technique

When ANN is constructed and designed for single output variable/parameter calculation as in FIG. 5 c, the total number of ANNs required for the unified functions of loadflow computation and contingency evaluations are 2(n−1) as there are two variables/parameters are to be calculated for each power network node. Similarly for of steady state voltage and angle stability calculations combined, total number of ANNs required are 2m. The input vector for all these [2(n−2)+2m] ANNs is the same of dimension 2n, which is prohibitively large for power networks of the order of 1000s of nodes. This is because the number of connection weights that must be determined in the training process increase with increasing number of input nodes. It will take a long time to train the ANN if there are a great number of inputs. In the worst case, the training process may fail to converge or may converge to local minimum that results in poor performance in the testing phase. Therefore it is essential to reduce the number of inputs to the ANN and retain only those system variables that have significant effects on the desired or target output. Feature selection is especially important when. we manage to apply ANN to a power system containing a great number of elements and variables. To train and finally store an ANN capable of yielding accurate estimates of voltage magnitudes, angles, V-stability index/margin, and θ-stability index/margin, it is essential to identify the key system features that affect these stated variables the most and employ the identified features as the inputs to the ANN. An approach based on system entropy is normally used as described in the available literature and in some of the reference cited in the above in this document. However, an invented approach is to use the technique of Suresh's diakoptics claimed in U.S. Pat. No. 7,788,051 dated Aug. 31, 2010: “Method and Apparatus for Parallel Loadflow Computation for Electric Power System”. The Suresh's diakoptics technique determines a sub-network for each node involving directly connected nodes referred to as level-1 nodes and their directly connected nodes referred to as level-2 nodes and so on., wherein the level of outward connectivity for a local sub-network around a given node whose single variable is to be estimated using separate ANN is to be determined experimentally. For example, an estimation of a node variable by a separate. ANN for each variable in 1000 node power system requires 2000 inputs. Whereas an invented approach stated in the above can reduce required inputs to about 200 by determining sub-network of may be say 5 to 20 level of outward connectivity around a node whose single variable is to be estimated using the separate ANN.

FIG. 6 is the overall integrated flow-chart of invented ANN Loadflow based security evaluation functions. Its separate steps are not elaborated and listed here because they are self explanatory based on above description and publicly available literature. Moreover, they do not form part of claims.

GENERAL STATEMENTS

The system stores a representation of the reactive capability characteristic of each machine and these characteristics act as constraints on the reactive power, which can be calculated for each machine.

While the description above refers to particular embodiments of the present invention, it will be understood that many modifications may be made without departing from the spirit thereof. The accompanying claims are intended to cover such modifications as would fall within the true scope and spirit of the present invention.

The presently disclosed embodiments are therefore to be considered in all respect as illustrative and not restrictive, the scope of the invention being indicated by the appended claims in addition to the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

REFERENCES Foreign Patent Document

1. U.S. Pat. No. 7,769,497 dated Aug. 3, 2010: “Method of Super Super Decoupled Load Flow Computation for Electric Power System”

2. U.S. Pat. No. 7,788,051 dated Aug. 31, 2010: “Method and Apparatus for Parallel Loadflow Computation for Electric Power System”

Published Pending Patent Application

3. Canadian Patent Application Number: CA2107388 dated 9 Nov. 1993: “System of Fast Super Decoupled Loadflow Calculation for Electrical Power System”

Other Publications

5. Fredric M. Ham and Ivica Kostanic, “Principles of Neurocomputing for Science and Engineering”, McGrow-Hill (2001)

6. Daniel Graupe, “Principles of Artificial Neural Networks”, World Scientific Publication (2007)

7. A. Jain, S. C. Tripathy, R. Balasubramanian, and Y. Kawazoe, “Stochastic Load Flow Analysis Using Artificial Neural Networks”, 2006 IEEE, pp. 1-6

8: A. Karami and M. S. Mohammadi, “Radial basis function neural network for power system load-flow”, Electrical Power and Energy Systems 30 (2008) 60-66

9. H. H. Muller, M. J. Rider and C. A. Castro, “Artificial neural networks for load flow and external equivalents studies”, Electric Power Systems Research (2010) article in press

10. S. B. Patel, “Fast Super Decoupled Loadflow”, IEE proceedings Part-C, Vol. 139, No. 1, pp. 13-20, Jan. 1992

11. S. B. Patel, “Super Super Decoupled Loadflow”, IEEE Toronto International Conference on Science and Technology for Humanity (IEEE TIC-STH 2009), September 2009, pp. 652-659. 

1. A method of forming/defining and solving a loadflow computation model of a power network to affect control of voltages and power flows in a power system, comprising the steps of: obtaining on-line/simulated data of open/close status of all switches and circuit breakers in the power network, and reading data of operating limits of components of the power network including maximum power carrying capability limits of transmission lines, transformers, and PV-node, a generator-node where Real-Power-P and Voltage-Magnitude-V are given/assigned/specified/set, maximum and minimum reactive power generation capability limits of generators, and transformers tap position limits, obtaining on-line readings of given/assigned/specified/set Real-Power-P and Reactive-Power-Q at PQ-nodes, Real-Power-P and voltage-magnitude-V at PV-nodes, voltage magnitude and angle at a reference/slack node, and transformer turns ratios, wherein said on-line readings are the controlled variables/parameters, performing loadflow computation to calculate, depending on training of the invented ANN loadflow computation model used, complex voltages or their real and imaginary components or voltage magnitude and voltage angle at nodes of the power network providing for calculation of power flow through different components of the power network, and to calculate reactive power generations at PV-nodes and reference/slack node, real power generation at the reference/slack node and transformer tap-position indications, training, testing and validating Neural Network Loadflow model for the purpose of performing said loadflow computation, generating training, testing and validating input-output data sets by applying uniform and non-uniform scaling factors applied to base case real and reactive power loads at PQ-nodes, resistance and reactance of transmission line branches, wherein the scale factors are increased until loadflow solution by conventional methods such as Newton-RaphsonLoadflow or Super Super Decoupled Loadflow methods diverge, and the divergence of loadflow methods are due to node voltage, node angle, and numerical instabilities, in addition to randomly generated data sets within the bounds of base case and values causing instabilities, wherein voltage magnitude and phase angle values in the solution before divergence are respective stability limits and voltage magnitude and phase angle values in loadflow solution provide direct measure to the respective stability margins, evaluating loadflow computation for any over loaded components of the power network and for under/over voltage at any of the nodes of the power network, correcting one or more controlled variables/parameters and repeating the performing loadflow computation by decomposing, initializing, solving, adding, counting, storing, evaluating, and correcting steps until evaluating step finds no over loaded components and no under/over voltages in the power network, and affecting a change in power flow through components the power network and voltage magnitudes and angles at the nodes of the power network by actually implementing the finally obtained values of controlled variables/parameters after evaluating step finds a good power system or stated alternatively the power network without any overloaded components and under/over voltages, which finally obtained controlled variables/parameters however are stored for acting upon fast in case a simulated event actually occurs.
 2. A method as defined in claim-1 wherein the ANN loadflow computation uses an entropy reduction technique of the Suresh's diakoptics that determines a sub-network for each node involving directly connected nodes referred to as level-1 nodes and their directly connected nodes referred to as level-2 nodes wherein the level of outward connectivity for a local sub-network around a given node whose single variable is to be estimated using separate ANN is to be determined experimentally for deciding the number of inputs for the separate ANN that estimates the single variable of the given node. 